i dont use facebook and don't really understand what is appealing about it the times I have seen it. Therapists are no different from anyone else and the idea that they across the board would not look clients up is, to me, just a completely silly idea. I don't see it as having anything to do with ethics in any realm.
The idea that therapists are busier, more ethical or more anything than any other working person is, to me, simply ridiculous.
I have never looked up a student or a client, but it is not for any manufactured "I am so very noble" reason - it is simply because I am not all that interested in them outside of my job. I have no reason to care what they posted or was on the internet about them.